Foundations of Probability

Abstract Probability, as a mathematical subject, is essentially unique and its formal rules are described. There are many different interpretations, of which three are mentioned: classical, frequentist, and in terms of belief. The many and varied justifications for thinking that beliefs should conform to the rules of probability, the Bayesian view, are described. The connections with decision‐making, the concept of utility, and the role of subjectivity are discussed. It is pointed out that the frequentist and Bayesian interpretations lead to distinct, practical implications of probability, especially in connection with the likelihood principle, and illustrations are provided. The role of exchangeability, which links the two views, is developed. Alternatives to probability are briefly mentioned.